Optics
For my money I want the best optics I can get. I hate fogged up or easily knocked out of alignment scopes. I also want it the most light gathering I can get. I disagree a lot on some recommendations on scopes above, for big game hunting you will probably never use a 9-12X on your scope. Those scopes are fine on varmit rifles they just don't get used in big game hunts.
My ideal scope is either a straight 4 power or a variable with 1.5x6. Anything above 4x it becomes almost impossible to make quick or running shots. Leupold, Ziess, Swarovski and Schmidt and Bender are all quality glass. I also like a slightly long eye relief. I have only one rifle with a higher powered scope nowdays, and it is a long range shooter. I have replaced all of the higher powered scopes with lower powers. It took me many years and a lot of hunts to figure this out. A 6x scope in dark timber is right on the edge of too much, you are compensating for the scope, 2-3X is much better. Don't expect this less power to save you much on money a straight leupold 4X is about $220, a 1.75x6Ex32mm long eye relief is around $450.00, for the others listed above expect to pay more a Ziess 1.25x4x24 is around $600.
My choice of rifles I will limit to new guns there are a lot of older rifles I like, but that will complicate this a lot.
1. Sako 75 Hunter, don't buy a magnum or your $ went immediatly close or to your 1K mark, but a 30-06, 7mm-08, 270 Win, 308 are all good calibers. I saw a new in box 75 hunter 30-06 for $799.00 on Gunsamerica. This with with a 4x Leupold above is right on your 1K, don't need rings as they come with quality set, you should be at around $1020.00. With the 30-06 and the right loads it is more than adequate for North American Hunting, granted a little light for big brown bears in close, and a little heavy on a small whitetail, but a little creativity with reloading can remedy all that, the bullet selection in 30 is the best what are we talking 110grs to 220grs that with the accuaracy of the Sako, one word SWEET.
2. If insist on a second choice I would consider a CZ or a Tikka. But only because I am sarificing quality for price.
Just cause I like them so much :
http://www.sako.fi/sako75_hunter.html
I also would not discount the 9.3 X 62 cartridge if I was really looking at bears and moose all the time, and never saw a whitetail ( I lived in Alaska for 5 Yrs ) this would be a definate serious contender.